Radical Functions & Transformations

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The general form is f(x) = √(x) or f(x) = n√(x) where n is a positive integer.

Front

What is the parent function of a square root function?

Back

The parent function of a square root function is f(x) = √(x). It has a domain of [0, ∞) and a range of [0, ∞).

Front

How does a vertical stretch affect the graph of a radical function?

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph steeper.

Front

What does a translation to the left by 2 units mean for the function f(x) = √(x)?

Back

The function becomes f(x) = √(x + 2), shifting the entire graph 2 units to the left.

Front

What is the effect of reflecting a radical function over the x-axis?

Back

Reflecting a radical function over the x-axis changes the function to f(x) = -√(x), flipping the graph upside down.

Front

What does a translation down by 2 units look like for the function f(x) = √(x)?

Back

The function becomes f(x) = √(x) - 2, shifting the entire graph down by 2 units.

Front

What is the transformation of f(x) = √(x) when it is reflected over the y-axis?

Back

The function becomes f(x) = √(-x), which reflects the graph across the y-axis.

Front

How do you identify the transformations of a function from its equation?

Back

Look for changes in the form f(x) = a√(bx - c) + d, where 'a' indicates vertical stretch/reflection, 'b' indicates horizontal stretch/compression, 'c' indicates horizontal translation, and 'd' indicates vertical translation.

Front

What is the effect of a horizontal translation of 3 units to the right on f(x) = √(x)?

Back

The function becomes f(x) = √(x - 3), shifting the graph 3 units to the right.

Front

What does a vertical compression by a factor of 1/2 mean for the function f(x) = √(x)?

Back

The function becomes f(x) = (1/2)√(x), making the graph less steep.